Finite Group Databasebeta

← #28402034

Subgroups — #28402034

Order 14464.

346 conjugacy classes of subgroups.

The subgroup lattice has 346 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299222C211yesmaximal, characteristic, complemented
2#20299213C211yesmaximal, characteristic, complemented
3#20298892C211yesmaximal, characteristic, complemented
4#20298890C211yesmaximal, characteristic, complemented
5#20298877C211yesmaximal, characteristic, complemented
6#20298845C211yesmaximal, characteristic, complemented
7#20298843C211yesmaximal, characteristic, complemented
8#20298840C211yesmaximal, characteristic, complemented
9#20298833C211yesmaximal, characteristic
10#20298821C211yesmaximal, characteristic, complemented
11#20298819C211yesmaximal, characteristic, complemented
12#20298813C211yesmaximal, characteristic, complemented
13#20298812C211yesmaximal, characteristic, complemented
14#20298623C211yesmaximal, characteristic, complemented
15#474×C113C211yesmaximal, characteristic, complemented
16C2×Dic452C2211yescharacteristic
17C2×#14268636C2211yescharacteristic
18C2×#14268635C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268630C2211yescharacteristic
21C2×C8×D113C2211yescharacteristic
22#16813621C2211yescharacteristic
23#16813617—21no—
24#16813615—21no—
25#16813611—21no—
26#16813610C2211yescharacteristic
27#16813609C2211yescharacteristic
28#16813608—21no—
29#16813607—21no—
30#16813605—21no—
31#16813602C2211yescharacteristic
32#16813602C2211yescharacteristic
33#16813601—21no—
34#16813598—21no—
35#16813597C2211yescharacteristic
36#16813593C2211yescharacteristic
37C4×Dic226C2211yescharacteristic
38#16813587C2211yescharacteristic
39#16813584C2211yescharacteristic
40#16813579C2211yescharacteristic
41#16813555C2211yescharacteristic
42#16813555C2211yescharacteristic
43C4⋊#11744751C2211yescharacteristic
44#16813551C2211yescharacteristic
45#16813551C2211yescharacteristic
46#16813547C2211yescharacteristic
47#16813545C2211yescharacteristic
48#16813545C2211yescharacteristic
49#16813545C2211yescharacteristic
50#16813544C2211yescharacteristic
51#16813542C2211yescharacteristic
52C4⋊Q8×C113C2211yescharacteristic
53C4×D4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C2×Dic226—21no—
60C2×Dic226C2311yescharacteristic
61C2×Dic226C2311yescharacteristic
62C2×D452—21no—
63C2×D452C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C4×D113—21no—
66C2×C4×D113C2311yescharacteristic
67Dic452—41no—
68#14268636—41no—
69#14268635—41no—
70#14268632—41no—
71#14268630—41no—
72C2×#11744751C2311yescharacteristic
73C2×#11744751C2311yescharacteristic
74C8×D113—41no—
75C4⋊Dic113—21no—
76C4⋊Dic113—21no—
77C4⋊Dic113C2311yescharacteristic
78#14268626—21no—
79#14268626—21no—
80#14268626—21no—
81#14268626D411yescharacteristic
82#14268626D411yescharacteristic
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624D411yescharacteristic
93#14268624D411yescharacteristic
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C2×Q8×C113—21no—
98C2×D4×C113C2311yescharacteristic
99C22×C4×C113—21no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113C2×D411yescharacteristic
111Q8×C113—81no—
112D4×C113—21no—
113D4×C113—21no—
114C2×C4×C113—21no—
115C2×C4×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—81no—
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2411yescharacteristic
121C22⋊D113—81no—
122C2×Dic113—21no—
123C2×Dic113—21no—
124C2×Dic113—21no—
125C2×Dic113C2×D411yescharacteristic
126C2×Dic113C2×D411yescharacteristic
127C2×Dic113C2×D411yescharacteristic
128D452—21no—
129D452—21no—
130D452—81no—
131C4×D113—21no—
132C4×D113—21no—
133C4×D113—81no—
134Dic226—21no—
135Dic226—21no—
136Dic226—21no—
137Dic226—21no—
138Dic226—81no—
139C8×C113—21no—
140C8×C113—21no—
141#11744751—21no—
142#11744751—21no—
143C22×C113—41no—
144C22×C113—41no—
145C22×C113—41no—
146C22×C113C22×D411yescharacteristic
147C2×D113—21no—
148C2×D113—21no—
149C2×D113—21no—
150C2×D113—41no—
151C2×D113—41no—
152C2×D113—41no—
153C4×C113—21no—
154C4×C113—21no—
155C4×C113—41no—
156C4×C113—41no—
157C4×C113—41no—
158C4×C113H(5,𝔽2)11yescharacteristic
159C4×C1132−1+411yescharacteristic
160Dic113—21no—
161Dic113—21no—
162Dic113—21no—
163Dic113—41no—
164Dic113—41no—
165Dic113—41no—
166C2×C113—81no—
167C2×C113#53711yescharacteristic
168C2×C113#57611yescharacteristic
169C2×C113#57811yescharacteristic
170D113—41no—
171D113—81no—
172#3262—1131nomaximal, Sylow
173C113#326211yescharacteristic, complemented, Sylow
174#542—1131no—
175#542—1131no—
176#477—1131no—
177#477—1131no—
178#474—1131no—
179#474D11311yescharacteristic, complemented
180#468—1131no—
181#468—1131no—
182#467—1131no—
183#466—1131no—
184#464—1131no—
185#464—1131no—
186#463—1131no—
187#463—1131no—
188#424—1131no—
189C2×Q16—1131no—
190C2×SD16—1131no—
191C2×SD16—1131no—
192C2×D8—1131no—
193C2×M16—1131no—
194C22×C8—1131no—
195C4⋊Q8—1131no—
196C4⋊Q8C2×D11311yescharacteristic
197#126—2261no—
198#126—2261no—
199#124—1131no—
200#124—1131no—
201#124—2261no—
202#124—2261no—
203#123—2261no—
204#123—2261no—
205C22⋊Q8—1131no—
206C22⋊Q8—1131no—
207C22⋊Q8—2261no—
208C22⋊Q8—2261no—
209#121—1131no—
210#121—1131no—
211C4×Q8—1131no—
212C4×Q8—1131no—
213C4×D4—1131no—
214C4×D4C2×D11311yescharacteristic
215#117—1131no—
216#107—1131no—
217#107—1131no—
218#107C2×D11311yescharacteristic
219#107C2×D11311yescharacteristic
220C4⋊C8—1131no—
221C4⋊C8—1131no—
222C4⋊C8—1131no—
223C4⋊C8C2×D11311yescharacteristic
224#103—1131no—
225#103—1131no—
226#103—1131no—
227#103—1131no—
228#102—1131no—
229#102—1131no—
230#102C2×D11311yescharacteristic
231#102C2×D11311yescharacteristic
232C2×Q8—21no—
233C2×Q8—1131no—
234C2×Q8—1131no—
235C2×Q8—2261no—
236C2×D4—1131no—
237C2×D4—2261no—
238C2×D4—2261no—
239C2×D4C22×D11311yescharacteristic
240C22×C4—21no—
241C22×C4—1131no—
242C22×C4—2261no—
243Q16—4521no—
244SD16—4521no—
245SD16—4521no—
246D8—4521no—
247M16—4521no—
248C2×C8—1131no—
249C2×C8—1131no—
250C2×C8—4521no—
251C2×C8C22×D11311yescharacteristic
252C2×C8C22×D11311yescharacteristic
253C4⋊C4—21no—
254C4⋊C4—1131no—
255C4⋊C4—1131no—
256C4⋊C4—1131no—
257C4⋊C4—2261no—
258C4⋊C4—2261no—
259C4⋊C4—2261no—
260C4⋊C4—2261no—
261C4⋊C4—2261no—
262C4⋊C4C22×D11311yescharacteristic
263C4⋊C4C22×D11311yescharacteristic
264C4⋊C4C22×D11311yescharacteristic
265C22⋊C4—21no—
266C22⋊C4—1131no—
267C22⋊C4—1131no—
268C22⋊C4—2261no—
269C22⋊C4—2261no—
270C22⋊C4—2261no—
271C22⋊C4—2261no—
272C22⋊C4—2261no—
273C22⋊C4—2261no—
274C22⋊C4—2261no—
275C22⋊C4—2261no—
276C22⋊C4—2261no—
277C42—1131no—
278C42—2261no—
279C42—2261no—
280C42C22×D11311yescharacteristic
281C23—21no—
282C23—1131no—
283C23—2261no—
284Q8—81no—
285Q8—9041no—
286Q8—2261no—
287Q8—2261no—
288Q8—2261no—
289Q8—2261no—
290D4—21no—
291D4—21no—
292D4—9041no—
293D4—9041no—
294D4—2261no—
295D4—2261no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—81no—
300C2×C4—1131no—
301C2×C4—1131no—
302C2×C4—1131no—
303C2×C4—9041no—
304C2×C4—2261no—
305C2×C4—2261no—
306C2×C4—2261no—
307C2×C4—2261no—
308C2×C4—2261no—
309C2×C4D4×D11311yescharacteristic
310C2×C4D4×D11311yescharacteristic
311C2×C4C23×D11311yescharacteristic
312C8—21no—
313C8—21no—
314C8—2261no—
315C8—2261no—
316C22—41no—
317C22—41no—
318C22—41no—
319C22—4521no—
320C22—4521no—
321C22—4521no—
322C22—2261no—
323C22—2261no—
324C22—2261no—
325C22C2×D4×D11311yescharacteristic
326C4—21no—
327C4—21no—
328C4—41no—
329C4—41no—
330C4—41no—
331C4—4521no—
332C4—4521no—
333C4—4521no—
334C4—2261no—
335C4—2261no—
336C4—2261no—
337C4#1681366811yescharacteristic
338C4#1681367011yescharacteristic
339C2—81no—
340C2—9041no—
341C2—4521no—
342C2#2029917811yescharacteristic
343C2#2029939911yescharacteristic
344C2#2029941411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#474×C113C2
socleC22×C113C22×D4
prime radical#20298833C2
hypercenter#474D113
hypocenterC113#3262
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #474

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. #20299222C2semidirect
2. #20299213C2semidirect
3. #20298892C2semidirect
4. #20298890C2semidirect
5. #20298877C2semidirect
6. #20298845C2semidirect
7. #20298843C2semidirect
8. #20298840C2semidirect
10. #20298821C2semidirect
11. #20298819C2semidirect
12. #20298813C2semidirect
13. #20298812C2semidirect
14. #20298623C2semidirect
15. #474×C113C2semidirect
173. C113#3262semidirect
179. #474D113semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202992222
#202992132
#202988922
#202988902
#202988772
#202988452
#202988432
#202988402
#202988332
#202988212
#202988192
#202988132
#202988122
#202986232
#474×C1132
#3262113